The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximu...The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood estimators of the parameters and their confidence intervals are derived. The expected time required to complete the life test under this censoring scheme is investigated. Finally, the numerical examples are given to illustrate some theoretical results by means of Monte-Carlo simulation.展开更多
This paper proposes a simple constant-stress accel- erated life test （ALT） model from Burr type XII distribution when the data are Type-I progressively hybrid censored. The maximum likelihood estimation （MLE） of t...This paper proposes a simple constant-stress accel- erated life test （ALT） model from Burr type XII distribution when the data are Type-I progressively hybrid censored. The maximum likelihood estimation （MLE） of the parameters is obtained through the numerical method for solving the likelihood equations. Approxi- mate confidence interval （CI）, based on normal approximation to the asymptotic distribution of MLE and percentile bootstrap Cl is derived. Finally, a numerical example is introduced and then a Monte Carlo simulation study is carried out to illustrate the pro- posed method.展开更多
Inference are considered for the dependence competing risks model by using the Marshal-Olkin bivariate exponential distribution. Under generalized progressively hybrid censoring with partially observed failure causes,...Inference are considered for the dependence competing risks model by using the Marshal-Olkin bivariate exponential distribution. Under generalized progressively hybrid censoring with partially observed failure causes, the maximum likelihood estimators are established, and the approximate confidence intervals are also constructed via the observed Fisher information matrix.Moreover, Bayes estimates and highest probability density credible intervals are presented and the importance sampling technique is used to compute corresponding results. Finally, the numerical analysis is proposed for illustration.展开更多
This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units re...This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units removed at each failure time follows the binomial distribution.The maximum likelihood estimation and the Bayesian estimation are derived.In the meanwhile,through a great quantity of Monte Carlo simulation experiments we have studied different hyperparameters as well as symmetric and asymmetric loss functions in the Bayesian estimation procedure.A real industrial case is presented to justify and illustrate the proposed methods.We also investigate the expected experimentation time and discuss the influence of the parameters on the termination point to complete the censoring test.展开更多
This paper considers the Bayesian and expected Bayesian（E-Bayesian） estimations of the parameter and reliability function for competing risk model from Gompertz distribution under Type-I progressively hybrid censori...This paper considers the Bayesian and expected Bayesian（E-Bayesian） estimations of the parameter and reliability function for competing risk model from Gompertz distribution under Type-I progressively hybrid censoring scheme（PHCS）. The estimations are obtained based on Gamma conjugate prior for the parameter under squared error（SE） and Linex loss functions. The simulation results are provided for the comparison purpose and one data set is analyzed.展开更多
Deep geothermal extraction processes expose rock masses to frequent and significant temperature fluctuations. Developing a comprehensive understanding of the shear fracture mechanisms and crack propagation behaviors i...Deep geothermal extraction processes expose rock masses to frequent and significant temperature fluctuations. Developing a comprehensive understanding of the shear fracture mechanisms and crack propagation behaviors in rocks under the influence of cyclic heating is imperative for optimizing geothermal energy extraction. This study encompasses several critical aspects under cyclic heating conditions, including the assessment of stress distribution states, the characterization of two-dimensional fracture paths, the quantitative analysis of three-dimensional damage characteristics on fracture surfaces, and the determination of the fractal dimension of debris generated after the failure of granite. The test results demonstrate that cyclic heating has a pronounced adverse effect on the physical and mechanical properties of granite. Consequently, stress tends to develop and propagate in a direction perpendicular to the two-dimensional fracture path. This leads to an increase in the extent of tensile damage on the fracture surface and accelerates the overall rock failure process. This increases the number of small-sized debris, raises the fractal dimension, and enhances the rock’s rupture degree. In practical enhanced geothermal energy extraction, the real-time monitoring of fracture propagation within the reservoir rock mass is achieved through the analysis of rock debris generated during the staged fracturing process.展开更多
基金supported by the National Natural Science Foundation of China(70471057)
文摘The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood estimators of the parameters and their confidence intervals are derived. The expected time required to complete the life test under this censoring scheme is investigated. Finally, the numerical examples are given to illustrate some theoretical results by means of Monte-Carlo simulation.
基金supported by the National Natural Science Foundation of China(7117116470471057)
文摘This paper proposes a simple constant-stress accel- erated life test （ALT） model from Burr type XII distribution when the data are Type-I progressively hybrid censored. The maximum likelihood estimation （MLE） of the parameters is obtained through the numerical method for solving the likelihood equations. Approxi- mate confidence interval （CI）, based on normal approximation to the asymptotic distribution of MLE and percentile bootstrap Cl is derived. Finally, a numerical example is introduced and then a Monte Carlo simulation study is carried out to illustrate the pro- posed method.
基金supported by the National Natural Science Foundation of China(11501433)the Fundamental Research Funds for the Central Universities(JB180711)
文摘Inference are considered for the dependence competing risks model by using the Marshal-Olkin bivariate exponential distribution. Under generalized progressively hybrid censoring with partially observed failure causes, the maximum likelihood estimators are established, and the approximate confidence intervals are also constructed via the observed Fisher information matrix.Moreover, Bayes estimates and highest probability density credible intervals are presented and the importance sampling technique is used to compute corresponding results. Finally, the numerical analysis is proposed for illustration.
基金supported by the National Statistical Science Research Project of China(2019LZ32)
文摘This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units removed at each failure time follows the binomial distribution.The maximum likelihood estimation and the Bayesian estimation are derived.In the meanwhile,through a great quantity of Monte Carlo simulation experiments we have studied different hyperparameters as well as symmetric and asymmetric loss functions in the Bayesian estimation procedure.A real industrial case is presented to justify and illustrate the proposed methods.We also investigate the expected experimentation time and discuss the influence of the parameters on the termination point to complete the censoring test.
基金supported by the National Natural Science Foundation of China(7117116471401134+1 种基金71571144)the Natural Science Basic Research Program of Shaanxi Province(2015JM1003)
文摘This paper considers the Bayesian and expected Bayesian（E-Bayesian） estimations of the parameter and reliability function for competing risk model from Gompertz distribution under Type-I progressively hybrid censoring scheme（PHCS）. The estimations are obtained based on Gamma conjugate prior for the parameter under squared error（SE） and Linex loss functions. The simulation results are provided for the comparison purpose and one data set is analyzed.
基金Project(52409132) supported by the National Natural Science Foundation of ChinaProject(ZR2024QE018) supported by the Natural Science Foundation of Shandong Province,China+2 种基金Project(BK20240431) supported by Basic Research Program of Jiangsu,ChinaProject(SNKJ2023A07-R14) supported by the Major Key Technical Research Projects of Shandong Energy Group,ChinaProject(2024M751813) supported by China Postdoctoral Science Foundation。
文摘Deep geothermal extraction processes expose rock masses to frequent and significant temperature fluctuations. Developing a comprehensive understanding of the shear fracture mechanisms and crack propagation behaviors in rocks under the influence of cyclic heating is imperative for optimizing geothermal energy extraction. This study encompasses several critical aspects under cyclic heating conditions, including the assessment of stress distribution states, the characterization of two-dimensional fracture paths, the quantitative analysis of three-dimensional damage characteristics on fracture surfaces, and the determination of the fractal dimension of debris generated after the failure of granite. The test results demonstrate that cyclic heating has a pronounced adverse effect on the physical and mechanical properties of granite. Consequently, stress tends to develop and propagate in a direction perpendicular to the two-dimensional fracture path. This leads to an increase in the extent of tensile damage on the fracture surface and accelerates the overall rock failure process. This increases the number of small-sized debris, raises the fractal dimension, and enhances the rock’s rupture degree. In practical enhanced geothermal energy extraction, the real-time monitoring of fracture propagation within the reservoir rock mass is achieved through the analysis of rock debris generated during the staged fracturing process.
